<html><head><title>Reflectivity Modelling Software</title>


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<h1>Relectivity Modelling Software</h1>

<h2>Associated Reading</h2>
<a href="http://www.crewes.org/Reports/2004/2004_13.pdf">Seismic modelling with the reflectivity method</a> by Yongwang Ma, Luiz Loures, and Gary F. Margrave<br>

<h2>Description</h2>
The software named 'reflectivity' is
used to model seismic wave propagation in stratified earth models. Files provided for
this release are located in the directory .../software/reflectivity. The main
program is named 'reflectivity.m'. Subroutines are (by order called):<br><br>

<table>
<tbody><tr bgcolor="#cccccc"><td>
    hanning_window.m
    </td><td>
    calculate tapering window for slowness and frequency
</td></tr>
<tr><td>
    slowness.m
    </td><td>
    convert wave velocities into squared slowness
</td></tr>
<tr bgcolor="#cccccc"><td>
    Rm_matrix.m
    </td><td>
    calculate the total reflection coefficient matrices between
    two interfaces
</td></tr>
<tr><td>
    RT.m
    </td><td>
    calculate reflection and transmission coefficient matrices across an
interface (called by Rm_matrix.m)
</td></tr>
<tr bgcolor="#cccccc"><td>
    free_surface.m
    </td><td>
    calculate reflection coefficient matrices at the free surface
</td></tr>
<tr><td>
    bessels.m
    </td><td>
    calculate Bessel's functions of the first kind (J0 and J1); this routine
runs faster than Matlab's built in Bessel function script (besselj.m).
</td></tr>
</tbody></table><br>

This code has been tested under MATLAB 7 (R14), running on both Microsoft
Windows and Linux platforms.<br><br>

As a function, 'reflectivity.m' requires three inputs, which
are vectors and matrices.  These variables can be loaded into the Matlab workspace
from parameter files residing in the directory. 'reflecivity_test.m' demonstrates one way to do this.
Three sample input files are given as examples; 1) model.dat, the earth model
used in modelling; 2) geometry.dat, receiver offsets; and 3) parameter.par, the physical
parameters used in modelling.<br><br>

<h2>Useful References</h2>
Aki, K., and Richards, P. G., 1980, Quantitative seismology, Theory and Methods:
Volume I: W. H. Freeman and Company.<br><br>
Kennett, B. L. N., 1983, Seismic wave propagation in stratified media: Cambridge
University Press.<br><br>
Ma, Y., Loures, L., and Margrave, G. F., 2004, Seismic modelling with the reflectivity method: CREWES
Research Report <strong>16</strong><br><br>
Muller, G., 1985, The relectivity method: a tutorial: J. Geophys., <strong>58</strong>, 153-174.<br><br>

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